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Abstract
A metal-dielectric-metal gradient phase partially reflecting surface based on the combination of a gradient index dielectric substrate with an inductive and a capacitive grids, is designed at microwave frequencies for antenna applications. The gradient index is obtained by realizing air holes of different dimensions in a dielectric host material. A prototype of the gradient index dielectric substrate is fabricated through three-dimensional printing, an additive fabrication technology. It is then associated to two patterned metallic grids to realize a partially reflecting surface with a gradient phase behavior. For experimental validation, the partially reflective surface is used as reflector in a low-profile Fabry-Perot cavity antenna. An angular enhancement of the emitted beam in a desired direction is reported by further engineering the phase introduced by the inductive and the capacitive grids. Far-field measurements are performed on fabricated antenna prototypes to validate the concept. Such gradient phase reflective surface paves the way to low-cost easy-made microwave metal-dielectric surfaces incorporating functionalities such as beam control, forming and collimation.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterials are periodically engineered structures made of metallic and/or dielectric constituents. The ability to control their unusual properties that are not observed with conventional materials available in nature, such as a negative, zero or less than unity refractive index give us an additional degree of freedom in controlling electromagnetic (EM) waves. At microwave frequencies, these properties have been extensively exploited for the design of novel electromagnetic devices, such as electromagnetic cloak [1], illusion devices [2–5], focusing devices [6–10], and antennas [11–14]. Since recently, planar two-dimensional (2D) versions of metamaterials known as metasurfaces have also been widely investigated to manipulate EM waves. They present the advantages of being low profile and showing low losses compared to bulk metamaterials. These advantages make metasurfaces more practical in antenna engineering applications [15–21]. More specifically, metasurfaces have been used as a partially reflective surfaces (PRS) in reflex-type Fabry-Perot (FP) cavity antennas to realize low-profile highly directive antennas [19–22]. Furthermore, gradient phase (GP) PRS achieved by either using non-uniform capacitive or inductive grid, have been exploited to produce beam steering [23–25].
In this paper, we propose a different concept to realize beam steering by making use of a thin gradient index (GRIN) dielectric substrate. The gradient index is obtained by making air holes in a dielectric host material and is fabricated by three-dimensional (3D) printing. The dielectric GRIN substrate is combined with two layers of copper strips, one acting as an inductive grid and the other one as a capacitive grid. This combination allows achieving a phase variation along the metal-dielectric thanks to the gradient index in the dielectric material. Such gradient phase medium used as partially reflective surface (PRS) in a low-profile FP cavity antenna provides the possibility to steer the radiated beam to an off-normal direction. Moreover, additional phase variation can be applied by engineering non-uniform capacitive or inductive grid on the dielectric GRIN substrate. Hence, high beam steering approaching 70° can be obtained with this accumulation phase approach in a thin Fabry-Perot cavity antenna. Finally, we demonstrate that beam steering can be cancelled when the influence of the GRIN substrate is compensated by applying a phase variation in the capacitive or inductive grid in the opposite direction. Full wave simulations based on finite element method are performed to validate the design method. Different prototypes are fabricated for experimental characterization. Reported experimental far-field radiation patterns agree qualitatively with simulations and validate the beam steering concept.
2. Engineering of gradient index substrate
The dielectric GRIN substrate is designed by spatially engineering the volume fraction of the dielectric in a host medium. Cylindrical holes of different geometrical dimensions are thus considered in a cubic dielectric unit cell, as illustrated in Fig. 1. Changing the radius r and thickness t of the dielectric allows to modify the effective permittivity εeff of the unit cell. The dielectric GRIN substrate is divided into six different regions, where a variation of εeff value from 1 to 2.8 is applied. For εeff values above 1, a host material of relative permittivity 2.8 is used and the desired εeff values are tailored by varying the volume fraction of the air holes in the host material. The unit cell of the dielectric cell and a schematic view of the dielectric GRIN substrate are shown in Fig. 1.
Fig. 1 Unit cell consisting of air hole in a dielectric host material and schematic design of the dielectric GRIN substrate.
Since dimensions of the unit cell are small compared to the free space wavelength λ0, the effective permittivity parameter εeff of the cell are obtained using the retrieval method described in [26] based on the inversion of reflection and transmission coefficients of an elementary cell. By judiciously adjusting the volume fraction of the air holes via the radius r and dielectric thickness t while keeping the periodicity p = 5 mm (λ0/12 at 5 GHz), εeff values are engineered. The reflection and transmission spectra of the metamaterial are calculated using commercial code HFSS from ANSYS Electromagnetics Suite [27] by applying the necessary periodic boundary conditions on a unit cell.
As it can be clearly observed in Fig. 2, an increase of the air hole radius r while keeping constant the periodicity p and dielectric thickness t in the cubic dielectric cell leads to a shift of the resonance towards higher frequencies. A larger air hole radius leads to a higher air volume fraction and therefore to a lower effective permittivity of the resulting cell. As such, resonance frequency shifts to higher frequencies. It can also be noted that a greater air volume fraction leads to a higher transmission level.
Fig. 2 Parametric study of the cubic dielectric unit cell where air hole radius r is changed, while p = 5 mm and t = 5 mm. (a) Reflection magnitude, R (dB). (b) Transmission magnitude, T (dB). (c) Reflection phase, R (deg). (d) Transmission phase, T (deg).
Conversely, an increase in thickness t of the dielectric while keeping periodicity p and air hole radius r constant causes an increase in the dielectric volume fraction and a decrease in air volume fraction. Therefore, resonance shifts towards lower frequencies due to an increase in effective permittivity of the resulting cell. As presented in Fig. 3, transmission level decreases due to higher contrast in permittivity between vacuum and the dielectric cell. It is also worthwhile to note that with such dielectric unit cell, only a small phase shift is noted at a specific frequency.
Fig. 3 (a) Parametric study of the cubic dielectric unit cell where dielectric thickness t is changed, while p = 5 mm and r = 2.1 mm. (a) Reflection magnitude, R (dB). (b) Transmission magnitude, T (dB). (c) Reflection phase, R (deg). (d) Transmission phase, T (deg).
The geometrical dimensions used in the different regions of the GRIN substrate shown in Fig. 1 are summarized in Table 1. Following the parametric studies reported in Figs. 2 and 3, the physical dimensions of the structure are optimized to operate around the frequency of 5 GHz.
Table 1. Geometrical Dimensions of Air Holes in Dielectric Host Materials and Resulting Effective Permittivity in the Different Regions of the Substrate
The lateral dimensions of the dielectric GRIN substrate are 20 cm × 20 cm and the substrate is simulated at 5 GHz. As it can be clearly observed in Fig. 1, regions 1 and 6 are 8 cm long along y-direction, whereas the other four regions are each 1 cm long. Regions 2 to 5 consist of 2 cells each while region 6 consists of 16 cells. Therefore under normal incidence, as illustrated in Fig. 4, the applied gradient index leads to a gradient phase along the substrate of 31° and 22° in reflection and transmission, respectively.
Fig. 4 Electromagnetic response at 5 GHz along the dielectric substrate. (a) Reflection magnitude, R (dB). (b) Transmission magnitude, T (dB). (c) Reflection phase, R (deg). (d) Transmission phase, T (deg).
3. Design of gradient phase partially reflecting surface for antenna applications
3.1 Gradient phase partially reflecting surface
The dielectric GRIN substrate is combined with two grids composed of 40 × 40 cells of copper strips, as presented in Fig. 5(a). The upper grid where the strips are oriented in the direction of the electric field E plays the role of an inductive grid. The lower grid with strips oriented in the direction of the magnetic field H represents a capacitive grid. Both grids are printed on a 0.2 mm thick epoxy substrate having relative permittivity εr = 3.9 and tangential losses tan δ = 0.02. The association of these two grids with the dielectric GRIN substrate allows producing an LC resonance. The metal-dielectric-metal unit cell is illustrated by the inset in Fig. 5(a).
Fig. 5 (a) Design of the dielectric GRIN substrate combined with inductive and capacitive grids. A description of the unit cell of the combined structure is given, where p = 5 mm, d = 5.4 mm. Magnitude (b) and phase (c) of the reflection and transmission coefficients when wl = 2.4 mm, wc = 4.6 mm, r = 2.1 mm and t = 1.6 mm.
A numerical analysis is performed on the unit cell together with appropriate boundary conditions. The different geometrical dimensions of the unit cell are: p = 5 mm, d = 5.4 mm, wl = 2.4 mm, wc = 4.6 mm, r = 2.1 mm and t = 1.6 mm. As presented in Figs. 5(b) and 5(c), a resonance is observed around 4.7 GHz, while providing a sufficiently high reflectance. The structure acts as an LC-resonant filter, which presents a reflection phase between 180° and −180°, depending on the frequency. We can also note a pass-band behavior where the transmission level is relatively low (about −19 dB).
By changing the permittivity of the dielectric substrate through a modification of geometrical parameters r and t, the resonance of the unit cell shifts in frequency. Thus the use of a GRIN substrate enables to create a phase gradient along the partially reflecting surface, necessary to produce beam steering.
3.2 Beam steering in Fabry-Perot cavity antenna
The GRIN substrate is realized using additive fabrication technology. The Objet Eden260VS 3D dielectric polyjet printer [28] is utilized for the printing process. A dielectric photopolymer having a dielectric permittivity of 2.8 similar to the host material of simulations is used. During the printing process, the air holes are filled with another material that is afterwards removed with water. A photography of the printed dielectric GRIN medium prototype is shown in Fig. 6(a). The uniform inductive and capacitive metasurfaces with geometrical parameters wl = 2.4 mm and wc = 4.6 mm as given in Table 2 for configuration A, are fabricated by chemical etching using classical printed circuit board technology and are shown in Figs. 6(b) and 6(c), respectively.
Fig. 6 (a) Photography of the fabricated dielectric GRIN substrate where εeff value varies from 1.13 to 2.8. (b) Photography of the fabricated inductive metasurface. (c) Photography of the fabricated capacitive metasurface. Zoomed details are shown in the insets.
Table 2. Geometrical Dimensions for the Different Antenna Configurations and Summary of the Deflection Angle Achieved. For All Configurations: εeff1 to εeff16 = 1, εeff17 to εeff18 = 1.13, εeff19 to εeff20 = 1.26, εeff21 to εeff22 = 1.75, εeff23 to εeff24 = 2.44, and εeff25 to εeff40 = 2.8.
The engineered GP PRS is used as reflector in a FP cavity antenna of lateral dimensions 20 cm × 20 cm, which is excited by a microstrip patch antenna fed by a radiofrequency connector. The patch antenna is printed over a 0.5 mm thick epoxy substrate (εr = 3.9 and tan δ = 0.02) backed by a 35 µm thick copper film. The PRS is placed at a distance h = 10 mm above the patch antenna source as depicted by the schematic diagram in Fig. 7(a), corresponding to λ/6 at 5 GHz. As illustrated in Fig. 7(b), the GP PRS presents a transmission phase variation ΔΨPRS of 41° along its surface at 4.93 GHz. It should be noted that here the gradient phase is only due to the variation of the index in the dielectric substrate. When a dielectric substrate with εr = 2.8 is used, a constant transmission phase of −25° is obtained. Full-wave simulations and direct far-field antenna measurements performed on the antenna prototypes show excellent agreement. The reflection coefficient S11 of the antenna shows good impedance matching with free space, as reported in Fig. 7(c). As shown in Fig. 7(d), the measured radiations patterns in the yoz plane at 4.93 GHz show a deflection angle of 27° of the main beam when the GP PRS is used in contrast to a normal beam in the case of a uniform PRS. Due to the imperfect measurement chamber where the ceiling and ground floor are not covered with microwave absorbers, ripples due to specular reflections on the uncovered surfaces appear in the experimental data.
Fig. 7 (a) Schematic view of the cavity composed of a PEC and a phase gradient PRS. (b) Transmission phase values along the uniform phase and gradient phase PRS. (c) S11 coefficient of the FP cavity antennas. (d) Far-field radiation patterns in the H-plane (yoz plane) showing beam deflection when using the GP PRS.
The beam steering observed with the GP PRS based Fabry-Perot cavity antenna can be explained using classical antenna array theory. If we consider the metasurface as an array of radiating micro-antennas, where each element is fed with a signal of distinct amplitude and phase, then the array factor AF is given as [29]
where N is the number of radiating elements (in our case the number of cells on the PRS, i.e. N = 40), k is the wavenumber at 5 GHz and p is the periodicity of the cells on the PRS (p = 5 mm). |En| and φn are respectively the amplitude and phase of the electric field along the PRS outside the cavity.The |En| and φn values are extracted from the electric field radiated by the FP cavity antenna in numerical simulations and are reported in Fig. 8(a). It is also important to note that the amplitude of the electric field is higher in the central zone of the PRS. This is due to the fact that we are in presence of a subwavelength cavity configuration and in such case, the central zone of the PRS is mainly illuminated by feeding source [30]. Moreover, even though refractive index of the dielectric substrate varies only in the middle of the PRS, the phase of the electric field varies along the whole PRS due to coupling between individual elements, as clearly depicted in Fig. 8(a). The radiation pattern calculated from (1) is presented in Fig. 8(b), where we can observe that the main beam is deflected away from the normal by an angle of 25°, which is very close to the steering angle observed from the FP cavity antenna. A larger beamwidth is obtained from antenna array theory since the metasurface is considered as an array of radiating elements without any ground plane and hence, as an array of dipoles. However, the approximation allows us justifying qualitatively the beam steering phenomena in the FP cavity antenna where a gradient phase PRS is used.
Fig. 8 (a) Amplitude (|En|) and phase (φn) values of the electric field along the gradient phase PRS. (b) The far-field radiation pattern calculated in the yoz plane using antenna array theory showing a beam deflection of 25°.
Though printed circuit board fabrication technology is well established for the design of the inductive and capacitive grids, dielectric 3D printing tolerance strongly depends on the deposited layer thickness accuracy of the printer. Such fabrication tolerance leads to a modification in the gradient index of the dielectric substrate of the PRS. If we consider an acceptable change in the gradient index resulting from slight modification of geometrical parameters r and t such that εeff values are 1.0, 1.2, 1.35, 1.96, 2.53 and 2.8 respectively in regions 1 to 6 of the GRIN substrate, then the influence on the steering performance is quasi-null as shown in Fig. 9.
Fig. 9 Influence of fabrication tolerance of the GRIN substrate on steering performance of the Fabry-Perot cavity antenna. In the original GP PRS, εeff values of the GRIN substrate are 1.0, 1.13, 1.26, 1.75, 2.44 and 2.8 whereas in the modified GP PRS, εeff values are 1.0, 1.2, 1.35, 1.96, 2.53 and 2.8.
3.3 Phase accumulation in the PRS
In this section, we discuss about the increase of phase variation in the PRS. Conversely to the previous section where uniform inductive and capacitive grids have been used, here different configurations combining uniform and non-uniform inductive and capacitive grids with the GRIN dielectric substrate are studied as partially reflective surfaces in the FP cavity antenna in order to evaluate the influence on the beam steering performances.
To evaluate the influence of the geometrical dimensions wl and wc of the inductive and capacitive grids on the transmission responses, parametric studies are performed on the PRS unit cell. The other geometrical dimensions of the unit cell are similar to those of Fig. 5. Figures 10(a) and (c) show that a change in the width wl of the inductive grid has little influence on the resonance frequency, but modifies considerably the transmission level. For instance, an increase in wl leads to a decrease in transmission and therefore to an increase in reflection. On the other hand, a change in the width wc of the capacitive grid has little influence on the transmission level, as illustrated in Fig. 10(b). However as shown in Figs. 10(b) and (d), when wc increases, intrinsic capacitance of the cell increases and therefore resonance shifts towards lower frequencies. A photography of the non-uniform fabricated grids is shown in Fig. 11.
Fig. 10 Parametric study of the metal-dielectric-metal unit cell composed of a dielectric and inductive and capacitive grids. (a) and (c) Transmission magnitude and phase for different values of wl. (b) and (d) Transmission magnitude and phase for different values of wc.
Fig. 11 (a) Photography of the fabricated non-uniform inductive grid where wl varies from 0.4 mm to 4.3 mm. (b) Photography of the fabricated non-uniform capacitive grid where wc varies from 4.6 mm to 4.9 mm.
We first start by replacing the uniform capacitive grid by a non-uniform one while keeping the uniform inductive grid in the GP PRS. The different geometrical dimensions of the grids are given for the antenna configuration B in Table 2. The variation of the strip width wc in the capacitive grid is gradually changed in the central region from cell 17 to cell 24, where the permittivity gradient is applied in the GRIN substrate. The phase gradient created by the non-uniform capacitive grid is oriented in the same direction as that of the GRIN dielectric substrate. Such configuration allows accumulating phase variations leading to a higher phase gradient in the PRS as displayed in Fig. 12(a). The simulated and measured radiation performances presented in Fig. 12(b) show a beam deflection of 40° at 4.4 GHz. The operation frequency is lower in this configuration due to the lower phase value at the center of the FP cavity. Indeed, the operating frequency of the antenna is related to the cavity height and reflection phase of the two reflectors (PEC and PRS). Therefore when phase increases, working frequency shifts downwards.
Fig. 12 (a) Transmission phase values along the gradient phase PRS for various PRS configurations. (b) Uniform inductive and non-uniform capacitive grids: 40° beam deflection. (c) Uniform capacitive and non-uniform inductive grids: 55° beam deflection (d) Non-uniform inductive and capacitive grids: 70° beam deflection. The far-field radiation patterns are plotted in the H-plane (yoz plane).
The second tested configuration consists in using the uniform capacitive grid with wc = 4.6 mm and the non-uniform inductive grid where wl varies from 0.4 mm to 4.3 mm along the metasurface as presented for configuration C in Table 2. A transmission phase variation of 56° is obtained at 5.4 GHz. The simulated and the measured radiation patterns presented in Fig. 12 (c) show a beam deflection angle close to 55°.
The last configuration for phase accumulation denoted as configuration D in Table 2 consists in using the non-uniform inductive and capacitive grids. The phase gradient achieved is about 78° at 5.4 GHz, as illustrated in Fig. 12(a). Simulated and measured far field radiation patterns presented in Fig. 12(d), show a very high beam steering approaching 70°. Such high value is quite difficult to attain with classical antenna arrays and has never been previously reached in a FP cavity antenna. The latter result proves that a high angle of deflection can be obtained by combining the phase gradient introduced by the non-uniform grids and the GRIN dielectric substrate. Furthermore, the ratio of directivity of the steered beam to that of the normally radiated beam is close to 80% for configuration B and drops down to 55% for the high deflection in configuration D as in the case of conventional phased-array antennas.
It is also worthwhile to note that instead of accumulating phase by combining non-uniform inductive and/or capacitive grids with the GRIN dielectric substrate, a higher phase gradient can also be obtained by combining uniform LC grids with a GRIN substrate using a high index host dielectric material. As shown in Fig. 7(b), when a host dielectric material of relative permittivity 2.8 is used, the transmission phase of the PRS with uniform LC grids varies from 2° to −39°. However, if a host dielectric material with relative permittivity of 10 is used, transmission phase of the PRS varies from 1° to −74°. Such phase gradient is very close to that of configuration D presented in Fig. 12, where non-uniform inductive and capacitive grids are simultaneously used with a GRIN substrate using a host dielectric material of permittivity 2.8. In the new configuration where uniform LC grids are combined with a GRIN substrate using a host dielectric material of relative permittivity 10, a high beam steering similar to configuration D is also obtained, as illustrated in Fig. 13.
Fig. 13 (a) Transmission phase values along the gradient phase PRS for various configurations. (b) Far-field radiation patterns in the H-plane (yoz plane) showing beam deflection when using the gradient phase PRS. High beam steering can also be obtained by combining uniform LC grids with a GRIN substrate using a high index host dielectric material.
3.4 Phase cancellation in the PRS
Finally we show that the gradient phase in the GRIN substrate can be compensated by applying another phase variation but in the opposite direction as illustrated in Fig. 14(a). The non-uniform inductive grid together with the uniform capacitive grid are utilized to achieve the phase cancellation. It is important to mention that the non-uniform inductive grid has not been particularly optimized to compensate exactly the phase gradient introduced by the GRIN dielectric substrate. Nevertheless, this combination is considered in order to show that the beam deflection of 27° initially obtained in configuration A with uniform inductive and capacitive grids can be reduced to nearly 0° as shown in Fig. 14(b). A complete cancellation of beam deflection should be obtained by optimizing the non-uniform inductive (or capacitive grid) such that no phase variation is achieved in the PRS.
Fig. 14 (a) Transmission phase values along the gradient phase PRS. (b) Far-field radiation patterns in the H-plane (yoz plane) showing beam deflection reduced to nearly 0°.
4. Conclusions
We have demonstrated high beam steering in a Fabry-Perot cavity antenna when using a gradient phase partially reflective surface incorporating a gradient index dielectric substrate. In this study, the gradient phase is basically obtained from a gradient index dielectric substrate combined with uniform inductive and capacitive LC resonant grids. The phase gradient can be further increased when non-uniform grids are used. A high angle of deflection approaching 70°, can then be effectively achieved by judiciously accumulating phase gradients introduced by non-uniform capacitive and inductive grids, and the GRIN dielectric substrate. Finally, we have shown the cancellation of beam deflection by a compensation of phase variation. The concept has been validated through calculated and measured far-field antenna patterns with a fairly good agreement.
In conclusion, this work shows that the concept of GRIN dielectric substrate can be a very effective low-cost solution to be used as a complementary device together with an active metasurface in a FP cavity antenna [31-32]. The active metasurface will then be able to provide phase gradient either for phase accumulation or for phase cancellation to respectively achieve high beam steering or boresight radiation (radiation along the normal) characteristics. The proposed GRIN dielectric substrate is easy to fabricate and presents potential airborne and trainborne applications in communication systems and environments where radiation direction needs to be controlled either in a passive way or electronically via the use of lumped components such as varactor diodes in the capacitive grid and nematic liquid crystals in the dielectric substrate. Moreover, such FP cavity concept can be extended to the optical domain where beam steering can be obtained through the use of microelectromechanical actuators [33].
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